On Eisenbud's and Wigner's R-matrix: A general approach

Details On Eisenbud's and Wigner's R-matrix: A general approach On Eisenbud's and Wigner's R-matrix: A general approach

2007-01-19

arxiv.org/abs/math-ph/0701052v1

J. Differ. Equations 244, 2545-2577 (2008)

Physics

Mathematical Physics

Scientific paper

10.1016/j.jde.2008.02.004

The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's $R$-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite deficiency indices. In the framework of boundary triplets and associated Weyl functions an abstract generalization of the $R$-matrix method is developed and the results are applied to Schr\"odinger operators on the real axis.

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